Palindromic Fraction

Algebra Level 1

$\frac { 666666\times 666666 }{ 1+2+3+4+5+6+5+4+3+2+1 }$

Find the value of the expression above.

12121212 14122141 12341234 12345654321

2 solutions

Ashish Menon
Mar 24, 2016

$\dfrac { 666666\times 666666 }{ 1+2+3+4+5+6+5+4+3+2+1 }$

= $\dfrac { 666666\times 666666 }{ 36 }$

= $\dfrac { 666666\times 666666 }{6×6}$

= $111111 × 111111$

= $12345654321$

Moderator note:

Simple standard solution.

did it the same way..

Satyabrata Dash - 5 years, 2 months ago

Great , cool

Ashish Menon - 5 years, 2 months ago

Why can't I simplify 666666*666666 to 666666 squared? I.e.

666666^2÷36=666666÷6? That equals 111111

Rafi Davis - 5 years, 2 months ago

how can u cancel out the powers when the bases are not equal

go through the exponential inequalities wiki once

Satyabrata Dash - 5 years, 2 months ago

I know I know I was being a bit of an idiot I forgot to square the root in it's simplified form of 1111 squared which would've given me the right answer

Rafi Davis - 5 years, 2 months ago

@Rafi Davis – Dont be short of yourself. I too have made a lot of mistakes, it is a continuous learning process. After commiting a mistakes we thinknof ourselves as idiot (I too have been a lot time in brilliant ;)). So, cheer up. :-)

Ashish Menon - 5 years, 2 months ago

@Ashish Menon – Thanks man😄

Rafi Davis - 5 years, 2 months ago

It is easy

Arun Garg - 5 years, 2 months ago

Why you give explanation it is so easy

Arun Garg - 5 years, 2 months ago

I appreciate your excitement, but the reason I gave the explanation is because not all of them know thus step. Somepeople may learn something knew. Thanks!

Ashish Menon - 5 years, 2 months ago

Akash Kagatikar
Mar 24, 2016

121=(22) (22)/(1+2+1)

12321=(333)

(333)/(1+2+3+2+1)
1234321=(4444) (4444)/(1+2+3+4+3+2+1) so on
12345654321=(666666) (666666)/(1+2+3+4+5+6+5+4+3+2+1)

Palindromic Fraction

2 solutions

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